Local Diffusion Coefficient Research Articles

A numerical and experimental validation of the room acoustics diffusion theory inside long rooms

The paper focuses on the validation of the recently proposed room-acoustics diffusion theory by means of numerical simulations and experimental measurements. The analysis aims to verify the equation underlying the theory (Fick’s law of diffusion) which relates the energy density gradient and the sound intensity inside a room through a constant diffusion coefficient. In this work, the acoustic quantities are numerically/experimentally derived under stationary conditions, and their ratio is employed to estimate the effective value of the diffusion coefficient inside long rooms. The numerical study was carried out with particle-tracing simulations. The measurements were performed with a Microflown® three-dimensional sound intensity probe inside a 1:16 scale model of a long room, varying the absorption and the scattering properties at the boundaries. A comparison between numerical and experimental results is carried out with a least-square algorithm, showing a fair agreement between the diffusion coefficients estimated with the two methods. The results lead to the conclusion that the reverberant sound field inside long rooms can be described by a non-homogeneous diffusion process: the local diffusion coefficient is not a constant inside the room but increases with the distance from the source and depends on the acoustical properties of the room boundaries.

Spatially Resolved Two-Color Diffusion Measurements in Human Skin Applied to Transdermal Liposome Penetration

A multiphoton excitation-based fluorescence fluctuation spectroscopy method, Raster image correlation spectroscopy (RICS), was used to measure the local diffusion coefficients of distinct model fluorescent substances in excised human skin. In combination with structural information obtained by multiphoton excitation fluorescence microscopy imaging, the acquired diffusion information was processed to construct spatially resolved diffusion maps at different depths of the stratum corneum (SC). Experiments using amphiphilic and hydrophilic fluorescently labeled molecules show that their diffusion in SC is very heterogeneous on a microscopic scale. This diffusion-based strategy was further exploited to investigate the integrity of liposomes during transdermal penetration. Specifically, the diffusion of dual-color fluorescently labeled liposomes--containing an amphiphilic fluorophore in the lipid bilayer and a hydrophilic fluorophore encapsulated in the liposome lumen--was measured using cross-correlation RICS. This type of experiment allows discrimination between separate (uncorrelated) and joint (correlated) diffusion of the two different fluorescent probes, giving information about liposome integrity. Independent of the liposome composition (phospholipids or transfersomes), our results show a clear lack of cross-correlation below the skin surface, indicating that the penetration of intact liposomes is highly compromised by the skin barrier.

Phase evolution and nature of oxide dissolution in metallurgical slags

The dissolution of solid lime particles into liquid slags at high temperatures was evaluated by means of confocal scanning laser microscopy. An additional solid layer around the lime particle was observed at the intermediate stage of the dissolution into CaOAl2O3SiO2 slags. The dissolution rate was decelerated due to the existence of the additional layer and the dissolution profile could be clearly distinguished into three stages, that is, an early, intermediate, and late stage. By adding 10 wt % MgO, this layer could be effectively eliminated and the slope of the whole dissolution profile kept relatively constant. The dissolution path and mechanisms were subsequently evaluated by incorporating thermodynamic calculations. Both direct and indirect dissolutions could be distinguished. It was realized that the decrease in composition range for solid precipitating after adding MgO could significantly reduce the interfacial reaction (IR) layer formation. Post‐mortem analyses on quenched samples were further carried out to confirm the theoretical calculations. It was found that the solid layer in slags without MgO was (CaO)2·SiO2 and (CaO)3·SiO2 which is in line with the thermodynamic calculations. However, only (CaO)2·SiO2 was noticed in slags with MgO which both (CaO)2·SiO2 and MgO phases should be present according to the calculations. The nonequilibrium during dissolution may play an important role on phase transformation and MgO particles in much smaller quantity may have dissolved into (CaO)2·SiO2 phase. The diffusion of CaO in both slags with and without MgO was additionally investigated. The local CaO concentration distributions from the direct dissolution phase to the slag bulk could be well fitted with the theoretical model proposed via Fick's second law. As a result, the local diffusion coefficient in the dissolution region was obtained and the effect of MgO addition on diffusion could be assessed. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2907–2916, 2013

Nonlinear Scaling of Surface Water Diffusion with Bulk Water Viscosity of Crowded Solutions

The translational hydration dynamics within 0.5-1.5 nm of the surface of a DPPC liposome, a model biomacromolecular surface, is analyzed by the recently developed Overhauser dynamic nuclear polarization (ODNP) technique. We find that dramatic changes to the bulk solvent cause only weak changes in the surface hydration dynamics. Specifically, both a >10-fold increase in bulk viscosity and the restriction of diffusion by confinement on a multiple nm length-scale change the local translational diffusion coefficient of the surface water surrounding the lipid bilayer by <2.5-fold. By contrast, previous ODNP studies have shown that changes to the biomacromolecular surface induced by folding, binding, or aggregation can cause local hydration dynamics to vary by factors of up to 30. We suggest that the surface topology and chemistry at the ≤1.5 nm scale, rather than the characteristics of the solvent, nearly exclusively determine the macromolecule's surface hydration dynamics.

Molecular Dynamics Simulations of Nanoparticle Interactions with a Planar Wall: Does Shape Matter?

AbstractWe investigate the hydrodynamic interactions of spherical colloidal nano particles and nano tetrahedra near a planar wall by means of molecular dynamics (MD) simulations of rigid particles within an all-atom solvent. For both spherical and nano-tetrahedral particles, we find that the parallel and perpendicular components of the local diffusion coefficient and viscosity, show good agreement with hydrodynamic theory of Faxén and Brenner. This provides further evidence that low perturbations from sphericality of a nanoparticle’s shape has little influence on its local diffusive behaviour, and that for this particular case, the continuum theory fluid dynamics is valid even down to molecular scales.

The speed of Arnold diffusion

A detailed numerical study is presented of the slow diffusion (Arnold diffusion) taking place around resonance crossings in nearly integrable Hamiltonian systems of three degrees of freedom in the so-called ‘Nekhoroshev regime’. The aim is to construct estimates regarding the speed of diffusion based on the numerical values of a truncated form of the so-called remainder of a normalized Hamiltonian function, and to compare them with the outcomes of direct numerical experiments using ensembles of orbits. In this comparison we examine, one by one, the main steps of the so-called analytic and geometric parts of the Nekhoroshev theorem. Thus: (i) we review and implement an algorithm Efthymiopoulos (2008) [45] for Hamiltonian normalization in multiply resonant domains which is implemented as a computer program making calculations up to a high normalization order. (ii) We compute the dependence of the optimal normalization order on the small parameter ϵ in a specific model and compare the result with theoretical estimates on this dependence. (iii) We examine in detail the consequences of assuming simple convexity conditions for the unperturbed Hamiltonian on the geometry of the resonances and on the phase space structure around resonance crossings. (iv) We discuss the dynamical mechanisms by which the remainder of the optimal Hamiltonian normal form drives the diffusion process. Through these steps, we are led to two main results: (i) We construct in our concrete example a convenient set of variables, proposed first by Benettin and Gallavotti (1986) [12], in which the phenomenon of Arnold diffusion in doubly resonant domains can be clearly visualized. (ii) We determine, by numerical fitting of our data, the dependence of the local diffusion coefficient D on the size ‖Ropt‖ of the optimal remainder function, and we compare this with a heuristic argument based on the assumption of normal diffusion. We find a power law D∝‖Ropt‖2(1+b), where the constant b has a small positive value depending also on the multiplicity of the resonance considered.

On the potential of the Cherenkov Telescope Array for the study of cosmic-ray diffusion in molecular clouds

Molecular clouds act as primary targets for cosmic-ray interactions and are expected to shine in gamma-rays as a by-product of these interactions. Indeed several detected gamma-ray sources both in HE and VHE gamma-rays (HE: 100 MeV < E < 100 GeV; VHE: E > 100 GeV) have been directly or indirectly associated with molecular clouds. Information on the local diffusion coefficient and the cosmic-ray population can be inferred from the observed gamma-ray signals. In this work we explore the capability of the forthcoming Cherenkov Telescope Array Observatory (CTA) to provide such measurements. We investigate the expected emission from clouds hosting an accelerator, surveying the parameter space for different modes of acceleration, age of the source, cloud density profile, and cosmic-ray diffusion coefficient. We present some of the most interesting cases for CTA regarding this science topic. The simulated gamma-ray fluxes depend strongly on the input parameters. In several cases, we find that it will be possible to constrain both the properties of the accelerator and the propagation mode of cosmic rays in the cloud from CTA data alone.

Fluorescence recovery after photo-bleaching as a method to determine local diffusion coefficient in the stratum corneum

Fluorescence recovery after photo-bleaching experiments were performed in human stratum corneum in vitro. Fluorescence multiphoton tomography was used, which allowed the dimensions of the photobleached volume to be at the micron scale and located fully within the lipid phase of the stratum corneum. Analysis of the fluorescence recovery data with simplified mathematical models yielded the diffusion coefficient of small molecular weight organic fluorescent dye Rhodamine B in the stratum corneum lipid phase of about (3–6)×10−9cm2s−1. It was concluded that the presented method can be used for detailed analysis of localised diffusion coefficients in the stratum corneum phases for various fluorescent probes.

Total Internal Reflection with Fluorescence Correlation Spectroscopy

The combination of total internal reflection illumination with fluorescence correlation spectroscopy (TIR-FCS) allows one to examine in quantitative detail a variety of biophysical properties related to the motions and interactions of fluorescent molecules near the interface of a transparent planar surface and an adjacent solution. Several experimental and theoretical aspects of this combination will be discussed. TIR-FCS has allowed characterization of local diffusion coefficients and concentrations of fluorescently labeled antibodies in solution but very close to substrate-supported phospholipid bilayers. TIR-FCS has also been used to examine the interaction kinetics of fluorescently labeled mouse IgG specifically and reversibly associating with the mouse receptor Fc-gamma-RII, which was purified and reconstituted into substrate-supported planar membranes. This method also has the potential, through the use of a single fluorescent reporter, of providing information about the thermodynamics/kinetics of nonfluorescent molecules which participate in surface binding mechanisms; e.g., those that compete with fluorescent reporters for surface-immobilized receptors or those that interact on the surface with the receptors and reduce or enhance the interaction of the fluorescent reporters with the surface binding sites.

Mapping CEACAM1 Dynamics and Interactions in Live Cells by Quantitative Fluorescence Techniques

Belonging to the immunoglobulin superfamily of membrane glycoproteins, carcinoembryonic antigen-related cell adhesion molecules (CEACAMs) are involved in diverse range of cellular processes and disease mechanisms through both homotypic and heterotypic interactions, In particular, CEACAM1 has been found to suppress tumorigenesis, hepatic lipogenesis, and systemic inflammation, but interestingly promotes tumour metastasis, angiogenesis, insulin clearance, and bacterial invasion. Molecular level insights into CEACAM1's behaviour are therefore essential for understanding its structure-function relationships. To this end, we have exploited high spatial- and temporal-resolution fluorescence imaging to elucidate the molecular dynamics and interactions of YFP-tagged CEACAM1 transfected into wild-type HeLa cells. Total internal reflection-fluorescence correlation spectroscopy (ITIR-FCS) enabled direct determination of the local diffusion coefficients of CEACAM1 in different regions of the cell membrane while number and brightness analysis (N&B) and spatial intensity distribution analysis (SpIDA) provided insights into the oligomeric state of CEACAM1. These strategies for characterizing the dynamics of transmembrane receptors in live cells show clear promise for probing glycoprotein function in normal and disease states.

Stellar diffusion in barred spiral galaxies

We characterize empirically the radial diffusion of stars in the plane of a typical barred disk galaxy by calculating the local spatial diffusion coefficient and diffusion time-scale for bulge-disk-halo N-body self-consistent systems which initially differ in the Safronov-Toomre-Q_T parameter. We find different diffusion scenarios that depend on the bar strength and on the degree of instability of the disk. Marginally stable disks, with Q_T \sim 1, have two families of bar orbits with different values of angular momentum and energy, which determine a large diffusion in the corotation region. In hot disks, Q_T> 1, stellar diffusion is reduced with respect to the case of marginally stable disks. In cold models, we find that spatial diffusion is not constant in time and strongly depends on the activity of the bar, which can move stars all over the disk recurrently. We conclude that to realistically study the impact of radial migration on the chemical evolution modeling of the Milky Way the role of the bar has to be taken into account.

Super-resolution surface mapping using the trajectories of molecular probes

The surface characterization of 'soft' materials presents a significant scientific challenge, particularly under 'wet' in situ conditions where a wide variety of non-covalent interactions may be relevant. Here we introduce a new chemical imaging method, MAPT (mapping using accumulated probe trajectories) that generates images of surface interactions by distributing different aspects of molecular probe trajectories into distinct locations and then combining many trajectories to generate spatial maps. The maps are super-resolution in nature, because they are accumulated from highly localized single-molecule observations. Unlike other super-resolution techniques, which report only photon or point counts, our analysis generates spatial maps of physical quantities (adsorption rate, desorption probability, local surface diffusion coefficient, surface coverage/occupancy) that are directly associated with the molecular interactions between the probe molecule and the surface. We demonstrate the feasibility of this characterization using a surface patterned with various degrees of hydrophobicity.

Density-Dependent Liquid Nitromethane Decomposition: Molecular Dynamics Simulations Based on ReaxFF

The decomposition mechanism of hot liquid nitromethane at various compressions was studied using reactive force field (ReaxFF) molecular dynamics simulations. A competition between two different initial thermal decomposition schemes is observed, depending on compression. At low densities, unimolecular C-N bond cleavage is the dominant route, producing CH(3) and NO(2) fragments. As density and pressure rise approaching the Chapman-Jouget detonation conditions (∼30% compression, >2500 K) the dominant mechanism switches to the formation of the CH(3)NO fragment via H-transfer and/or N-O bond rupture. The change in the decomposition mechanism of hot liquid NM leads to a different kinetic and energetic behavior, as well as products distribution. The calculated density dependence of the enthalpy change correlates with the change in initial decomposition reaction mechanism. It can be used as a convenient and useful global parameter for the detection of reaction dynamics. Atomic averaged local diffusion coefficients are shown to be sensitive to the reactions dynamics, and can be used to distinguish between time periods where chemical reactions occur and diffusion-dominated, nonreactive time periods.

Determination of spatially-resolved porosity, tracer distributions and diffusion coefficients in porous media using MRI measurements and numerical simulations

This work is focused on measuring the concentration distribution of a conservative tracer in a homogeneous synthetic porous material and in heterogeneous natural sandstone using MRI techniques, and on the use of spatially resolved porosity data to define spatially variable diffusion coefficients in heterogeneous media. The measurements are made by employing SPRITE, a fast MRI method that yields quantitative, spatially-resolved tracer concentrations in porous media. Diffusion experiments involving the migration of H(2)O into D(2)O-saturated porous media are conducted. One-dimensional spatial distributions of H(2)O-tracer concentrations acquired from experiments with the homogeneous synthetic calcium silicate are fitted with the one-dimensional analytical solution of Fick's second law to confirm that the experimental method provides results that are consistent with expectations for Fickian diffusion in porous media. The MRI-measured concentration profiles match well with the solution for Fick's second law and provide a pore-water diffusion coefficient of 1.75×10(-9)m(2)s(-1). The experimental approach was then extended to evaluate diffusion in a heterogeneous natural sandstone in three dimensions. The relatively high hydraulic conductivity of the sandstone, and the contrast in fluid density between the H(2)O tracer and the D(2)O pore fluid, lead to solute transport by a combination of diffusion and density-driven advection. The MRI measurements of spatially distributed tracer concentration, combined with numerical simulations allow for the identification of the respective influences of advection and diffusion. The experimental data are interpreted with the aid of MIN3P-D - a multicomponent reactive transport code that includes the coupled processes of diffusion and density-driven advection. The model defines local diffusion coefficients as a function of spatially resolved porosity measurements. The D(e) values calculated for the heterogeneous sandstone and used to simulate diffusive and advective transport range from 5.4×10(-12) to 1.0×10(-10)m(2)s(-1). These methods have broad applicability to studies of contaminant migration in geological materials.

Colloidal diffusion inside a spherical cell

The hydrodynamic hindering of a single-particle dynamics under total confinement is measured by optical microscopy. The three-dimensional trajectories of single-colloidal particles confined in spherical water globules of sizes only a few times the particle's diameter are tracked as they sample the entire volume of the globule. The hydrodynamic interactions between the particle and the spherical wall produce a dependence of the short-time diffusion on the particle's distance to the surface and an asymmetry in the radial and tangential components of the local diffusion coefficient, with the diffusion along the tangential direction being faster than along the radial direction. The latter decreasing close to the wall while the former being practically constant.

Estimation and Inference of Diffusion Coefficients in Complex Biomolecular Environments.

The 1-D diffusion coefficient associated with a charged atom fluctuating in an ion-channel binding pocket is statistically analyzed. More specifically, unconstrained and constrained molecular dynamics simulations of potassium in gramicidin A are studied. Time domain transition density based inference methods are used to fit simple stochastic differential equations and also to carry out frequentist goodness of fit tests. Particular attention is paid to varying the time between adjacent time series observations due to the well-known "non-Markovian noise" that can appear in this system due to inertia and other unresolved coordinates influencing the dynamics. Different types of non-Markovian noise are shown by the goodness of fit tests to be statistically significant on vastly different time scales. On intermediate scales, a Markovian model is not rejected by the tests; models calibrated at these intermediate scales demonstrate a predictive capability for some physical quantities. However, in this intermediate regime, ergodic sampling does not occur over the length of a time series, but a local diffusion coefficient is deemed statistically acceptable for the observed raw data. It is demonstrated that a linear mixed effects model can be used to summarize the variation induced by slow unresolved degrees of freedom acting as a non-Markovian noise source. The utility of quantitative criteria for assessing low-dimensional stochastic models calibrated from time series generated by high-dimensional biomolecular systems is briefly discussed. Less coarse-grained data summaries of this type show promise for better understanding the kinetic signature of unresolved degrees of freedom in time series coming from simulations and single-molecule experiments.

Dynamics and state of lipid bilayer-internal water unraveled with solution state 1H dynamic nuclear polarization

The dynamics and state of lipid bilayer-internal hydration water of unilamellar lipid vesicles dispersed in solutions is characterized. This study was enabled by a recently developed technique based on Overhauser dynamic nuclear polarization (DNP)-driven amplification of (1)H nuclear magnetic resonance (NMR) signal of hydration water. This technique can, in the full presence of bulk water, selectively quantify the translational dynamics of hydration water within ∼10 Å around spin labels that are specifically introduced to the local volume of interest within the lipid bilayer. With this approach, the local apparent diffusion coefficients of internal water at different depths of the lipid bilayer were determined. The modulation of these values as a response to external stimuli, such as the addition of sodium chloride or ethanol and the lipid phase transitions, that alter the fluctuations of bilayer interfaces together with the activation energy values of water diffusivity shows that water is not individually and homogeneously solvating lipid's hydrocarbon tails in the lipid bilayer. We provide experimental evidence that instead, water and the lipid membrane comprise a heterogeneous system whose constituents include transient hydrophobic water pores or water structures traversing the lipid bilayer. We show how these transient pore structures, as key vehicles for passive water transport can better reconcile our experimental data with existing literature data on lipid bilayer hydration and dynamics.

Diblock copolymer membranes investigated by single-particle tracking

We report a study on particle diffusion in membranes formed from polystyrene-block-poly(2-(dimethylamino)ethyl methacrylate) (PS-b-PDMAEMA) diblock copolymers. The membranes were investigated by scanning electron microscopy and by single-particle tracking employing carboxy-functionalized polystyrene beads loaded with a fluorophore as spectroscopic probes. From the diffusion trajectories we extracted the domain size distribution of the membranes and the local diffusion coefficient of the beads as a function of the size of the beads. The single-particle tracking data revealed that the effective domain sizes of the membranes are reduced with respect to the domain sizes obtained from scanning electron microscopy, reflecting the confined diffusion of the probe particles due to interactions with the domain walls. This is corroborated by a clear correlation between the diffusion coefficient of an individual polystyrene bead and the size of the actual domain to which it is confined.

Water-proton-spin–lattice-relaxation dispersion of paramagnetic protein solutions

The paramagnetic contributions to water-proton-spin–lattice relaxation rate constants in protein systems spin-labeled with nitroxide radicals were re-examined. As noted by others, the strength of the dipolar coupling between water protons and the protein-bound nitroxide radical often appears to be larger than physically reasonable when the relaxation is assumed to be controlled by 3-dimensional diffusive processes in the vicinity of the spin label. We examine the effects of the surface in biasing the diffusive exploration of the radical region and derive a relaxation model that incorporates 2-dimensional dynamics at the interfacial layer. However, we find that the local 2-dimensional dynamics changes the shape of the relaxation dispersion profile but does not necessarily reproduce the low-field relaxation efficiency found by experiment. We examine the contributions of long-range dipolar couplings between the paramagnetic center and protein-bound-water molecules and find that the contributions from these several long range couplings may be competitive with translational contributions because the correlation time for global rotation of the protein is approximately 1000 times longer than that for the diffusive motion of water at the interfacial region. As a result the electron–proton dipolar coupling to rare protein-bound-water-molecule protons may be significant for protein systems that accommodate long-lived-water molecules. Although the estimate of local diffusion coefficients is not seriously compromised because it derives from the Larmor frequency dependence, these several contributions confound efforts to fit relaxation data quantitatively with unique models.

Diffusion of Neutral and Ionic Species in Charged Membranes: Boric Acid, Arsenite, and Water

Dynamic ion speciation using DMT (Donnan membrane technique) requires insight into the physicochemical characteristics of diffusion in charged membranes (tortuosity, local diffusion coefficients) as well as ion accumulation. The latter can be precluded by studying the diffusion of neutral species, such as boric acid, B(OH)₃⁰(aq), arsenite, As(OH)₃⁰(aq), or water. In this study, the diffusion rate of B(OH)₃⁰ has been evaluated as a function of the concentration, pH, and ionic strength. The rate is linearly dependent on the concentration of solely the neutral species, without a significant contribution of negatively charged species such as B(OH)₄⁻, present at high pH. A striking finding is the very strong effect (factor of ~10) of the type of cation (K(+), Na(+), Ca(2+), Mg(2+), Al(3+), and H(+)) on the diffusion coefficient of B(OH)₃⁰ and also As(OH)₃⁰. The decrease of the diffusion coefficient can be rationalized as an enhancement of the mean viscosity of the confined solution in the membrane. The diffusion coefficients can be described by a semiempirical relationship, linking the mean viscosity of the confined solute of the membrane to the viscosity of the free solution. In proton-saturated membranes, as used in fuel cells, viscosity is relatively more enhanced; i.e., a stronger water network is formed. Extraordinarily, our B(OH)₃-calibrated model (in HNO₃) correctly predicts the reported diffusion coefficient of water (D(H₂O)), measured with ¹H NMR and quasi-elastic neutron scattering in H(+)-Nafion membranes. Upon drying these membranes, the local hydronium, H(H₂O)(n)(+), concentration and corresponding viscosity increase, resulting in a severe reduction of the diffusion coefficient (D(H₂O) ≈ 5-50 times), in agreement with the model. The present study has a second goal, i.e., development of the methodology for measuring the free concentration of neutral species in solution. Our data suggest that the free concentration can be measured with DMT in natural systems if one accounts for the variation in the cation composition of the membrane and corresponding viscosity/diffusion coefficient.